When Trees Collide: An Approximation Algorithm for the Generalized Steiner Problem on Networks

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SIAM Journal on Computing, ISSN: 0097-5397, Vol: 24, Issue: 3, Page: 440-456

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Agrawal, Ajit; Klein, Philip; Ravi, R.
Society for Industrial & Applied Mathematics (SIAM); SIAM
Computer Science; Mathematics; approximation algorithm; network design; Steiner tree problem; Economic Policy; Economics; Industrial Organization
article description
We give the first approximation algorithm for the generalized network Steiner problem, a problem in network design. An instance consists of a network with link-costs and, for each pair {i, j} of nodes, an edge-connectivity requirement r. The goal is to find a minimum-cost network using the available links and satisfying the requirements. Our algorithm outputs a solution whose cost is within 2[log(r + 1)] of optimal, where r is the highest requirement value. In the course of proving the performance guarantee, we prove a combinatorial min-max approximate equality relating minimum-cost networks to maximum packings of certain kinds of cuts. As a consequence of the proof of this theorem, we obtain an approximation algorithm for optimally packing these cuts; we show that this algorithm has application to estimating the reliability of a probabilistic network.